1. Field of the Invention
This invention relates to a method and apparatus for determining accurately an interstitial oxygen concentration in a silicon single crystal.
2. Description of the Prior Art
Heretofore, the Czochralski (CZ) method has been adopted for the operation of pulling a silicon single crystal. It has been known that this method requires use of a crucible made of quartz for accomodating a molten silicon mass and that this method, therefore, entails a possibility that the oxygen contained in the crucible of quartz will be melted out and passed into the molten silicon mass and eventually incorporated in the silicon single crystal. The oxygen which is thus incorporated into the silicon single crystal persists in the form of an interstitial oxygen in the silicon single crystal. Some oxygen atoms collect into clusters and persist in a precipitated state.
The oxygen which thus persists in the silicon single crystal at times forms a defect which induces an impairment of the characteristic properties of a transistor as a device using the silicon single crystal and at other times produces an useful effect as in manifesting a gettering effect or enhancing mechanical strength of a wafer in the production of an integrated circuit. Thus, the desirability of developing a technique for accurately determining the interstitial oxygen concentration ("Oi") in a silicon single crystal has been finding growing recognition. Particularly for the purpose of coping with the high degree of integration prevailing recently, the "Oi" in the single crystal Si substrate to be used must be controlled accurately on the order of 0.1 ppma or the order of 0.01 ppma. Thus, a need is felt strongly for a method and apparatus which determines the "Oi" with high accuracy enough to suit the evaluation aimed at.
Heretofore, for the determination of the interstitial oxygen concentration [Oi] in a silicon single crystal, the method which relies on the absorption of the interstitial oxygen in the infrared local vibration mode, namely the method which effects the determination of the interstitial oxygen concentration by finding the light absorption coefficient .alpha..sub.o of the interstitial oxygen [Oi] with respect to the absorption peak at 1106 cm.sup.-1 at normal room temperature and multiplying the light absorption coefficient .alpha..sub.o by the concentration conversion coefficient k as shown below. EQU [Oi]=k.alpha..sub.0 [Formula 1.]
has been known as the most fundamental of all the methods known in the art.
In accordance with a report by Japan Electronic Industry Development Association (JEIDA) [T. Iizuka et al., J. Electrochem. Soc., 132, 1707(1985)], the concentration conversion coefficient k is 3.03.times.10.sup.17 cm.sup.-2. The light absorption coefficient .alpha..sub.o is the physical quantity which is substantially proportional to the peak height of Oi absorption at 1106 cm.sup.-1 as reported by T. Iizuka et al.. More specifically, it is the physical quantity which is found by correcting the slight deviation from the relation of proportions caused by the effect of multiple reflection within a given sample in accordance with the following formulas 2 and 3 using such parameters as the peak height and the sample thickness. In other words, the coefficient .alpha..sub.o can be determined by the method (JEIDA method) reported in the literature mentioned above.
For the determination of [Oi] of a Si crystal, the net infrared light transmittance T of the Oi local vibration is expressed under the existence of internal multiple reflection effect by the formula 2: EQU T=f(R, d, .alpha..sub.1, .alpha..sub.o)e.sup.-.alpha..sbsp.o.sup.d[Formula 2]
In the formula shown above, f(R,d,.alpha..sub.1, .alpha..sub.o) is expressed by the following formula 3. ##EQU1##
In the formula 3 shown above, R stands for the reflectance on the surface of the Si crystal which is R=0.30, d for the thickness of the oxygen-containing sample crystal and the reference crystal having an oxygen concentration below the lower limit of detection, .alpha..sub.1 for the light absorption coefficient based on the vibration of the Si crystal lattice which is .alpha..sub.1 =0.85 cm.sup.-1, and .alpha..sub.o or the light absorption coefficient based on the local vibration of interstitial oxygen atoms.
The determination of the net transmittance T is carried out as follows. First, the spectrum of the value T.sub.sample /T.sub.reference which is obtained by dividing the transmittance T.sub.sample of the oxygen-containing sample crystal by the transmittance T.sub.reference of the reference crystal, namely the comparative spectrum. FIG. 4 shows the comparative spectrum in the Oi absorption wavelength range. In the diagram, the ratio T.sub.peak /T.sub.base i.e. the ratio of the peak value T.sub.peak to the base value T.sub.base in the Oi absorption forms the net transmittance T in the Oi local vibration (in other words, T=T.sub.peak /T.sub.base).
In addition to the JEIDA method otherwise called A method described above, the method to be described herein below (B method) has been widely used in the industry for the determination of [Oi]. The formula 2 described above differs exclusively by the factor portion of the function for correction of multiple reflection, f(R,d,.alpha..sub.1 .alpha..sub.o), from the following Lambert-Beer's law which holds good on the assumption that no multiple reflection occurs within a given sample. EQU T=e.sup.-.alpha.d [Formula 4]
The B method presumes that the following formula 5 of approximation to which the Lambert-Beer's law applies with necessary modifications holds good. EQU T.apprxeq.e.sup.-.alpha..sbsp.o,eff.sup.d.sbsp.eff [Formula 5]
In the formula d.sub.eff stands for the effective thickness of the sample. The reason for using the effective thickness d.sub.eff in the place of the actual sample thickness d in the formula 5 of approximation is that the effective length of light path is increased owing to the multiple reflection of the infrared light within the crystal as illustrated by way of a model in FIG. 5 and the effective thickness d.sub.eff consequently becomes somewhat larger than the actual thickness d.
This effective thickness d.sub.eff can be empirically fixed as a physical quantity which is proportionate to the peak height (p) of the LO+LA phonon at 738 cm.sup.-1 in the absorbance spectrum (A.sub.sample =log [1/T.sub.sample ]) of the sample crystal illustrated in FIG. 6, for example. In other words, the following expression is presumed. EQU d.sub.eff, (Constant).times.(Peak height p of LO+LA phonon)[Formula 6]
By substituting the d.sub.eff found as described above and the net transmittance T due to the Oi vibration in the formula 5, the following formula 7 is derived regarding the effective absorption coefficient of Oi is fixed by the following formula 7. ##EQU2##
The interstitial oxygen concentration [Oi] is evaluated in accordance with the following formula 8, using the effective concentration conversion coefficient k.sub.eff which is fixed by the .alpha..sub.o/eff and the physical quantity of concentration found by measurment. EQU [Oi].apprxeq.k.sub.eff .alpha..sub.o,eff [Formula 8]
Since this method of determination utilizes the effective thickness d.sub.eff to be found by the method of infrared absorption as shown in the formula 6 and therefore obviates the necessity for measuring the actual sample thickness d, it is widely used in the industry on account of the advantage that it allows automatic measurement which renders unnecessary the measurement of thickness. This method, however, permits no exact evaluation of [Oi] because the formula 5 presumed by the method is only an approximation of the formula 2 for compensation of multiple reflection.